Question

Consider two firms (Firm A and Firm B) competing in this market. They simultaneously decide on the price of the product in a typical Bertrand fashion while producing an identical product. Both firms face the same cost function: C(qA) = 12qA and C(qB) = 12qB, where qA is the output of Firm A and qB is the output of Firm B. The demand curve is P = 30 - Q.
(i) What will be the Bertrand-Nash equilibrium price (pB) chosen by each firm? Explain.
(ii) What is the equilibrium quantity (qB) sold by each firm and the total market output
(QN)?
(iii) What, if any, is the dead-weight loss in this case?

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Now consider a typical Cournot duolpoly situation such that the market is being served by two firms (Firm 1 and Firm 2) that simultaneously decide on the level of output to sell in the market while producing an identical product. The total output is Q = q1 + q2 and each firm has a cost function of C(q1) = 12q1 and C(q2) + 12q2

(i) What is the inverse market demand function and the profit function for both firms?

(ii) Derive the reaction functions for Firm 1 and Firm 2 .

(iii) What is the Cournot-Nash equilibrium output level (qn) for each firm?

(iv) Calculate the market price of the product (pn).

(v) What will the total market output (Qn) be for both firms together?

(vi) Calculate the allocated inefficiency resulting from this market situation.

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Please include explanatory graphs in all answers.

Answer 1